Contents Online
Mathematical Research Letters
Volume 19 (2012)
Number 2
Global well–posedness and scattering for the defocusing, cubic NLS in $\mathbb{R}^3$
Pages: 431 – 451
DOI: https://dx.doi.org/10.4310/MRL.2012.v19.n2.a14
Author
Abstract
We prove global well-posedness and scattering for the defocusing, cubic NLS on $\mathbb{R}^3$ withinitial data in $H^s(\mathbb{R}^3)$ for $s>49/74$. The proof combines the ideas of resonancedecomposition in \cite{CKSTT4} and linear–nonlinear decomposition in \cite{ben1,roy} togetherwith the idea of large time iteration.
Published 12 July 2012